Chessette By Craig Anderson CURSOR 2, no. 4 (November/December 1980): 76-77.
This is a simple, two-player-only version of Chess for the Bally Arcade/Astrocade. The pieces are drawn to the screen and the players each take turns moving them using special to/from notation. Read the complete documentation for Chessette in the Cursor newsletter to understand the rules.
This video shows a complete, 6-move game: ending with a trapped queen:
Sandor Takacs vs Josef Emil Krejcik Vienna blitz (1920), Vienna AUT
This video is broken into several parts. Here is a breakdown of the entire video to make viewing it easier to find what you're looking for in this video:
0:00 - Chessette, Overview of game 2:57 - Chessette - Running and playing the game 5:54 - Chessette - BASIC Program Listing 7:01 - End Credits
Chessette runs in only 1.8K of RAM. It's a simple, but effective proof-of-concept as to whether a chess game with graphics could be created on the Astrocade.